Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊#11759967 |
| unambiguous semidirect product | D257⋊(C4⋊C4) |
| Fitting | C2×C4×C257 ⋊ C4 |
| Sylow | C257 ⋊ C2×C4⋊C4 |
92 conjugacy classes of subgroups.
532 conjugacy classes — view the full character table.
| maximal subgroup of | #30657610, #30657611, #30657616, … |
| maximal normal subgroup of | #30657610, #30657611, #30657616, … |
| maximal quotient of | C2×(C2×#11759967)⋊C4, C4×C4⋊#11759967, #30657679, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 224);